| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.12.25 |
$8$ |
$x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$12$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[4/3, 4/3, 2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.12.26 |
$8$ |
$x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$12$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[4/3, 4/3, 2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.57 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$16$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.58 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$8$ |
$1$ |
$16$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.59 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 4 x + 10$ |
$2$ |
$8$ |
$1$ |
$16$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 6 x^{2} + 4 x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.16.60 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 10$ |
$2$ |
$8$ |
$1$ |
$16$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[4/3, 4/3, 3]$ |
$[4/3, 4/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 2 x^{2} + 4 x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
| 2.8.18.63 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 6$ |
$2$ |
$8$ |
$1$ |
$18$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[2, 8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 6$ |
$[11, 11, 4, 0]$ |
$[1, 1]$ |
| 2.8.18.64 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[2, 8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{3} + 2$ |
$[11, 11, 4, 0]$ |
$[1, 1]$ |
| 2.8.18.65 |
$8$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{3} + 6$ |
$2$ |
$8$ |
$1$ |
$18$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[2, 8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{3} + 6$ |
$[11, 11, 4, 0]$ |
$[1, 1]$ |
| 2.8.18.66 |
$8$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{3} + 2$ |
$2$ |
$8$ |
$1$ |
$18$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[2, 8/3, 8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{3} + 2$ |
$[11, 11, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.63 |
$8$ |
$x^{8} + 4 x^{5} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 4 x^{2} + 10$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.64 |
$8$ |
$x^{8} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 4 x^{2} + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.65 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 10$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.66 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.67 |
$8$ |
$x^{8} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.68 |
$8$ |
$x^{8} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 10$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.69 |
$8$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{2} + 10$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
| 2.8.20.70 |
$8$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$S_4\times C_2$ (as 8T24) |
$2$ |
$3$ |
$[8/3, 8/3, 3]$ |
$[8/3, 8/3, 3]_{3}^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 4 x^{2} + 2$ |
$[13, 10, 8, 0]$ |
$[1, 1]$ |
